Michelle was instructed to write two equivalent expressions for 6x + 15.


Her work is shown.


6x + 15 = x + x + x + x + x + x + 15


6x + 15 = 6(x + 15)


Part A: Explain which one of Michelle’s equations is true for all values of x and which one of Michelle’s equations is false for all values of x. (2 pts.)


Part B: Write another equivalent expression for 6x + 15.

Answer:

Step-by-step explanation:

V=15

fraction of cylinder volume is=22

Answer:

hi i can help you if you want just text

The function f(x) = xlnx is decreasing on the open interval (0, e^-1).

To find the interval on which the function f(x) = xlnx is decreasing, we need to find the intervals where the first derivative f'(x) is negative.

Using the product rule of differentiation, we can find the first derivative of f(x) as

f'(x) = x × (1/x) + ln(x) × 1 = 1 + ln(x)

Now, we need to find the values of x where f'(x) < 0

1 + ln(x) < 0

ln(x) < -1

x < e^-1

Therefore, f(x) is decreasing on the interval (0, e^-1).

Note that we exclude x = 0 from the interval because the function is not defined for x ≤ 0.

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Answer:

x = 21

Step-by-step explanation:

(4x+11°) = (5x-10)

4x + 11 = 5x - 10

-x + 11 = -10

-x = -21

x = 21

Answer:

Step-by-step explanation:

1)Move all x terms to one side

11° = x - 10°

2)Move all constant terms to the other side

11° + 10° = x - 10° + 10°

21° = x

So the solution to the equation is x = 21°.

The two solutions that satisfy the equation 3x^2 + 2x = 6 when rounded to two decimal places are x = 1.12 and x = −1.79. So, correct option is A.

To solve for x in the equation 3x^2 + 2x = 6, we need to rearrange the terms and use the quadratic formula:

3x^2 + 2x - 6 = 0 (subtract 6 from both sides)

x = (-b ± √(b^2 - 4ac)) / 2a (quadratic formula)

In this equation, a = 3, b = 2, and c = -6, so we can substitute those values into the quadratic formula:

x = (-2 ± √(2^2 - 4(3)(-6))) / 2(3)

x = (-2 ± √(4 + 72)) / 6

x = (-2 ± √(76)) / 6

Simplifying this expression, we get:

x = (-2 ± 2√(19)) / 6

x = (-1 ± √(19)) / 3

Rounding these solutions to two decimal places, we get:

x = -1.79 or x = 1.12

Therefore, the answer is (a) x = 1.12 and x = -1.79.

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Answer:

x = 1.12 and x = −1.79

Step-by-step explanation:

i got it right on my quiz

The z-score of a car that is 6 years old is  -0.625.

To find the z-score of a car that is 6 years old, we can use the formula:

z = (x - μ) / σ

where x is the value we are interested in (in this case, 6 years old), μ is the mean of the distribution (8 years), and σ is the standard deviation (3.2 years).

Plugging in the values, we get:

z = (6 - 8) / 3.2 = -0.625

Therefore, the z-score of a car that is 6 years old is -0.625. This indicates that the car is 0.625 standard deviations below the mean age of cars driven by employees at the company. Since the distribution is normal, we can use this z-score to find the probability of finding a car with an age of 6 years or less, using a z-table or a calculator.

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The exact length of arc AB is π feet. To round to the nearest hundredths, we get:

AB ≈ 3.14 feet

What is a circle?

It is the center of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.

we can use the central angle and the fact that a full circle has a central angle of 360° to calculate the fraction of the circumference that AB represents.

Since the central angle, APB is 45°, we can calculate the fraction of the circumference that AB represents as:

45°/360° = 1/8

Therefore, AB represents 1/8 of the circumference of the circle.

If we let C be the circumference of the circle, then the length of AB can be calculated as:

AB = (1/8) * C

Since we do not know the value of C, we cannot calculate the exact length of AB. However, we can leave our answer in terms of π as:

AB = (1/8) * π * d

where d is the diameter of the circle.

If the diameter of the circle is 8ft, then the radius (r) is half of that, or 4ft. We can now use this value to find the exact length of AB.

The circumference (C) of the circle can be found using the formula:

C = 2πr

where π is the constant pi.

Plugging in the given value of the radius, we get:

C = 2π(4ft) = 8πft

Therefore, the exact length of AB is:

AB = (1/8) * C = (1/8) * 8π ft = π ft

Hence, the exact length of arc AB is π feet. To round to the nearest hundredths, we get:

AB ≈ 3.14 feet

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Answer:

color cube

Step-by-step explanation:

The best approximation for the p-value for the test statistic t0 = 2.155 is 0.032.

To find the best approximation for the p-value for the hypothesis test with null hypothesis H0: μ=8 and alternative hypothesis H1: μ>8, with variance unknown and n=10, and a test statistic t0=2.155, we need to use the t-distribution with degrees of freedom (df) equal to n-1 = 10-1 = 9.

The p-value is the probability of obtaining a test statistic as extreme or more extreme than the observed one, assuming the null hypothesis is true. Since this is a one-tailed test with the alternative hypothesis in the form of μ>8, the p-value corresponds to the area in the right tail of the t-distribution.

Using a t-table or calculator with the t-distribution, we can find the probability of obtaining a t-value as large as 2.155 or larger with 9 degrees of freedom. This probability is approximately 0.032. Therefore, the best approximation for the p-value for this hypothesis test is 0.032.

We can interpret this result as follows: if the null hypothesis is true (i.e., if the population mean is 8), the probability of obtaining a sample mean as extreme or more extreme than the observed one (i.e., greater than 8.215) is 0.032. Since this probability is relatively small, we may reject the null hypothesis in favor of the alternative hypothesis at a significance level of 0.05 or smaller.

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The following probabilities are found under the condition that  a certain national survey of heads of households P(woman asked for a promotion) = 24%, P(woman received promotion, given she asked for one) = 45%, P(woman asked for promotion and received raise) = (24% x 45%) = 10.8%

Now,
Regarding  a national survey concerning the head od households,  only 24% of women interviewed had requested for a promotion and of those women who had asked for a promotion, 45% received the raise.

Therefore,

(a) P(woman asked for a promotion) = 24%
(b) P(woman received promotion, given she asked for one) = 45%
(c) P(woman asked for promotion and received raise) = (24% x 45%) = 10.8%

Probability refers to the percentage of an event taking place in a required time frame, in a specified place. It is considered a great aid in the fields of science and mathematics.

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Jim's daily income must be less than $2 in order for him to be considered impoverished.

Income is an entity's ability to save and spend money during a given period of time, and it usually appears in terms of money. In principle, income can be hard to establish, and there may be variations depending on the field.

According to the World Bank's definition, there are two categories for impoverished people's salaries:

a) Moderate Poverty - A person is deemed to be in moderate poverty if their daily income is less than $2.

b) Extreme Poverty - While a person is deemed to be living in extreme poverty if they make less than 1.2 dollars per day.

Jim's daily wage must be less than $2 in order for him to be classified as impoverished.

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He run on Thursday is 3.75 miles.

Algebra helps in converting a mathematical statement into an equation. We know if we have ‘more’ or ‘sum’ in the given sentence we use addition operation (+) . Similarly If we have ‘less’ or ‘difference’ we use subtraction (−) . If we have a ‘quotient’ we use division operation (÷) . To define more generalized terms; we use algebra. It is a very vast branch of mathematics and is used in all the branches of mathematics like polynomial, linear equations, graphs, etc. and in daily life too.

Now, Gavriel ran 5 miles on Wed

and,  On Thursday, he ran 3/4 as far.

We have to find the how far did he run on Thursday.

On Thursday , The distance will be:

=> 5 × 3/4

=> 15/4

=> 3.75 miles

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Answer: Permutation: A permutation is an course of action of a set of objects in a particular arrange. The number of conceivable changes of a set of n objects is n factorial (n!), which is the item of all positive integrability up to n.

Factorial: The factorial of a non-negative numbers n is signified by n! and is characterized as the item of all positive integrability less than or rise to to n. For case, 5! = 5 x 4 x 3 x 2 x 1 = 120.

Series: A arrangement may be a entirety of terms organized in a particular arrange. The entirety of the terms in a arrangement is called its add up to.

Circular permutation: A circular stage may be a stage of a set of objects in a circular course of action, where the arrange of objects things, but the beginning point is subjective. For case, orchestrating the letters A, B, and C in a circle would result in 3 circular stages: ABC, BCA, and CAB. The number of conceivable circular stages of a set of n objects is (n-1)!.

Step-by-step explanation:

We can deduce here that the experimental probability that the next time Lea rolls the number cubes, they will land with a 1 showing on the top face of one number cube and a 5 showing on the top face of the other number cube is: 1/36.

Probability is a measure for determining the possibility or chance that a specific event will take place. It is typically stated as a number between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty.

We can see that there is only one roll where one number cube that shows a 1 and the other number cube shows a 5. Therefore, the number of successful outcomes is 1.

The total number of rolls seen are: 36 rolls = 6 possible outcomes on the first number cube × 6 possible outcomes on the second number cube.

We can then see here that the probability will be = 1/36.

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The Complement of a 14° angle is 76°, while the supplement of 14° angle is 166°.

Recall that two angles that have a sum of 90 degrees are referred to as complementary angles. This implies that, if x is an angle, its complement is (90 - x).

Also, the supplement of an angle is the angle measure that is added to it to make it 180 degrees. This implies that if x is an angle, its supplement would be (180 - x).

Therefore, we have:

Complement of a 14° angle = 90 - 14 = 76°.

Supplement of 14° angle = 180 - 14 = 166°.

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Given the above conditions in the word problem above, x is also equal to 6.5°.

The angle x is the angle between this perpendicular line and the Earth's surface. It is also equal to the angle between the tangent line and the horizontal axis.

Since the reentry angle is 6.5°, we know that the tangent line makes an angle of 6.5° with the horizontal axis. We also know that the tangent line and the perpendicular line form a right angle, so the angle between the perpendicular line and the horizontal axis is 90° - 6.5° = 83.5°.

Finally, we can subtract this angle from 90° to find x:

x = 90° - 83.5° = 6.5°

Therefore, x is also equal to 6.5°.

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The evaluated probabilities for the given question are 0.20 for the men who asked for promotion, 0.59 for the men who received the promotion when asked, and  0.118 for men who asked for promotion and received.under the condition that from the men interviewed  20% had asked for a promotion and 59% of the men who had asked for a promotion and  received.
Then,
P(man asked for a promotion)
= 20/100
= 0.20

P(man received promotion, given he asked for one)
= 59/100
= 0.59

P(man asked for promotion and received )
= P(man asked for a promotion) x P(man received promotion, given he asked for one)
= 0.20 x 0.59
= 0.118
Probability is considered as  the percentage of an event taking place in a specific time frame, in a given place. It is said to be a great aid in the horizons of science and mathematics.


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Answer:

x= 64/ 7

Step-by-step explanation:

3/8x - 6 = 1/2(4 - x)

3/8x - 6 = 2- 1/2 x

3/8x - 8 = - 4/8 x

so 7/8 x = 8

x = 64/7

Answer:is this an actual question

Step-by-step explanation:

The correct alternative hypothesis for the Wilcoxon rank sum test is: ha: one distribution is shifted in a location higher or lower than the other. Option C is the answer.

This means that the test is designed to determine if there is a significant difference between the medians of two independent groups, rather than testing for a difference in means.

The null hypothesis for the test is that there is no significant difference between the two groups, while the alternative hypothesis states that there is a significant difference.

The Wilcoxon rank sum test is a nonparametric test and is used when the assumptions of the t-test are not met, such as non-normality or unequal variances.

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Answer:

57

Step-by-step explanation:

2 X 2 = 4

4 X 8 = 32

32 + 25 = 57

The factored form of the expression x² + 5x+6 is (x + 3)(x + 2)

To factorize the quadratic equation, we need to take the following steps;

Multiply the coefficient of the x squared by the constant value, we have;

6

Now, find the pair factors of the product that would add up to give 5, we have;

2 + 3

Substitute the values into the expression, we have;

x² + 2x + 3x + 6

Now, group the expression in pairs, we have;

(x² + 2x) + (3x + 6)

Factorize the expressions

x(x + 2) + 3(x + 2)

Then, we have;

x + 3

x + 2

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Answer: The compound interest is $409.49, and the total amount after one year is $3,665.49.

Step-by-step explanation:

We can use the formula for compound interest to solve this problem:

A = P(1 + r/n)^(nt)

where:

P = the principal (in this case, $3,256)

r = the annual interest rate (100%, or 1 as a decimal)

n = the number of times the interest is compounded per year (4, since it's compounded quarterly)

t = the number of years (1)

Plugging in the values we know, we get:

A = $3,256(1 + 1/4)^(4*1)

A = $3,256(1.25)^4

A = $3,665.49 (rounded to the nearest cent)

To find the compound interest, we can subtract the principal from the total amount:

Compound interest = $3,665.49 - $3,256 = $409.49

Therefore, the compound interest is $409.49, and the total amount after one year is $3,665.49.

The percentage of students at the school who describe their parents or guardians as "strict" is the key statistic. 2. A sample survey is the ideal research design for this project.

Since it would be impractical to poll all 1000 kids at the school, the students intend to collect data from a sample of students in order to concentrate on the strict guardians, which is a population parameter.

The sample proportion could be used by the students as a statistic to determine this population proportion. They can ask a sample of pupils drawn at random from the school whether they think their parents or guardians are "strict". The percentage of sample kids who respond "yes" can be used to approximate the percentage of school-wide students who view their parents or guardians as "strict". A statistic that offers an estimate of the population parameter of interest is the sample proportion.

Random sampling would be a suitable technique for generating a sample of 100 pupils. Each kid in the school might be given a number, and the pupils could then use a random number generator to choose 100 numbers from the list. The chosen students might then be contacted and asked to take part in the study. This technique lessens the possibility of bias in the sample selection process and aids in ensuring that the sample is representative of the population.

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1) The value of an equation for y in terms of x is, y = 1/5x

And, y = 20 at x = 100

2) y = 184.8 , at x = 14

The value of an equation for y in terms of x is, y = 13.2x

Given that;

1) y is directly proportional to x.

2) y ∝ x and y=132 when x=10

Now, For 1;

1) Since, y is directly proportional to x.

Hence, We get;

y = kx

Plug y = 5 and x = 25

5 = 25k

k = 1/5

Hence, The value of an equation for y in terms of x is,

y = 1/5x

And, Plug x = 100,

y = 1/5 x 100

y = 20

2) Since,  y ∝ x and y=132 when x=10

y = kx

132 = 10k

k = 13.2

Hence, At x = 14;

y = 13.2 x 14

y = 184.8

Thus, The correct equation is,

y = 13.2x

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A computation time expression ~ n, of means that the computation time increases in proportion to the size of the input.

This presents a computational complexity of O(n). Here 'O' stands for 'Big O Notation' and is used to denote an upper bound on the computational complexity of the algorithm.

That's, the algorithm's computational complexity is straightforwardly corresponding to the measure of the input information.

This shows that as the input estimate increments, the computational time will increment at the same rate.

 Linear time complexity is considered to be very efficient, and many algorithms aim to achieve this level of complexity. This is a relatively efficient computational complexity and is common in algorithms that require only one pass through the input data. 

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Answer:

10

Step-by-step explanation:

Answer:

There are 20 R100 notes and 80 R50 notes.

Step-by-step explanation:

Let's call the number of R100 notes "x" and the number of R50 notes "4x" (since there are 4 times as many R50 notes as R100 notes).

We can set up an equation to represent the total value of the notes:

100x + 50(4x) = 6000

Simplifying:

100x + 200x = 6000

300x = 6000

x = 20

So there are 20 R100 notes and 4 times as many R50 notes:

4x = 4(20) = 80

Therefore, there are 20 R100 notes and 80 R50 notes.